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I was reading a book comparison topic which stated that Zorich's Analysis is a pretty good substitute for spivak+rudin, in that if you don't have the time then reading Zorich's Analysis can compensate for both of these books (and probably more since it's very comprehensive). This makes sense, because seeing as it was written for first year Russian students, it doesn't expect you to have completely mastered calculus, so it starts very concretely with calculus but slowly the abstraction builds up until it's much more abstract than Rudin by the end of volume 2.

Now I was thinking, is there a similar book like that for Algebra? It would be great if I could skip a first year algebra course by reading an Algebra book like Zorich, because I don't enjoy "first courses" too much and even Littlewood discouraged reading "first course" -type books (Fraleigh is a good example of one today) in his Miscellany.

More concretely, the question is this: Is there a comprehensive Algebra book that starts very concretely, say first year material, but then develops to become at least as abstract as say second or third year material? Preferably with hard problems like in Zorich. Such a book would save my time and I'm sure many others'.

Edit: Just to show I've tried answering this, I've found three books so far: Artin's Algebra, Cameron's Intro to Algebra, and Norman's Undergraduate Algebra. Artin could definitely work but I don't know enough about it to make that judgement; Cameron is a bit too slim but apparently covers first, second and even some third year level material in UK universities; Norman is a bit too concrete (many practical applications) so doesn't fit the criteria of being abstract enough, and the problems aren't too challenging.

Thanks

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  • $\begingroup$ I used Zorich 1 & 2 in my first year analysis course and hated it. It is rather dense and contains way to much for a first year course. I would compare Zorich with something like Algebra from Lang. A book that I do like is Abstract Algebra from Dummit and Foote. It covers a lot of basic abstract algebra, but with many examples and exercises. $\endgroup$ – Noud Sep 30 '15 at 11:31
  • $\begingroup$ @Noud: but zorich is actually written for undergraduates. $\endgroup$ – user45220 Sep 30 '15 at 12:18
  • $\begingroup$ yes, I know. Abstract Algebra from Dummit and Foote is also for undergraduates. $\endgroup$ – Noud Oct 1 '15 at 14:45
  • $\begingroup$ @Noud: thanks I'll check it out $\endgroup$ – user45220 Oct 1 '15 at 18:12
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We use Kostrikin's Introduction to Algebra here in China. We use Zorich for calculus too and I feel they have a somewhat similar style. Try it out, but I think the English version may be fairly old. The latest Russian edition is the 3rd edition.

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